Transforming energy with magnetism Magnetic Induction Transforming energy with magnetism

Lorentz Force Reminder F = qv  B Source: Griffith, The Physics of Everyday Phenomena F is directed out of the screen.

CPS Question What is the direction of the Lorentz force on the charges moving in this wire? B A. D. B. E. C. F. I

Current in a Field Feels a Force B F I

Circuit in a Field Has Torque B I I

Torque Turns a Motor I current I force F B

Moving Creates an EMF – B v + induced potential

Notice the direction B I A current moved the wire The motion created an emf opposing the current that initiated it!

Moving conductor Each charge receives a force qvB Conductor becomes polarized Potential inside a conductor!?

Moving conductor Force F = qvB Work w = (qvB)·L Potential e = (vB)·L Notice: L  v and L  B so, L || vB Optimal orientation!

Why “EMF”? It definitely is electromotive It’s not a force. Units V = J/C Not a potential: not a conservative force So we just call it “emf,” never mind the origin

Aside: Scalar Triple Product (A  B)  C volume of parallelepiped defined by A, B, C Equivalent to (B  C)  A (C  A)  B B A C

Rotating Loop Creates Current B V V

Rotating Loop Creates Current B V V

Rotation Powers a Generator v Motion B through the field V induces a potential which generates a current that charges the battery

Magnetic Flux Field through a surface F = BA Effectively the number of field lines enclosed by a loop

Group Work a b c d e At which position(s) does the most magnetic flux pass through the loop? At which position(s) is the magnetic flux through the loop changing the fastest?

Flux Change Creates Emf Faraday’s Law Changing the magnetic flux through a loop creates an emf around the loop. e = –DF Dt

Magnetic Flux Flux changes as loop turns b c d e Flux changes as loop turns At a, c, e: Greatest flux F, least change At b, d: Zero flux, fastest flux change DF/Dt

Induced current direction Lenz’s Law The current induced by changing the magnetic flux inside a circuit generates a magnetic field that opposes the change.

Lenz’s Law Explains Generator changing field e opposing field B needed I

Group Work What is the Lorentz force on each side? Which direction is the flux change? What current would oppose it? B If the loop inside this magnetic field expands, in what direction will the induced current be?

Group Work Which direction is the flux change? What current would oppose it? B If the magnetic field becomes weaker, in what direction will the induced current be?

How a Microphone Works microphone geophone Flux inside loop becomes more

Wave-Powered Generator Originally appeared in Smithsonian magazine.

How a Loudspeaker Works induced motion of magnet current-generated field attracts or repels magnet current

AC Transformers Source: OSHA

Flux Change Creates Emf Rapidly changing field high induced emf unchanging field zero induced emf

How a Transformer Works AC current in the primary coils creates a changing magnetic field. The magnetic flux inside the secondary coils changes Changing flux induces emf in the secondary coils

Potential Proportional to Loops Same flux F through both sets of windings Each loop adds emf Emf’s V are proportional to the number of loops N V1 N1 V2 N2 =

Energy is Conserved Ideally: power in = power out V1I1 = V2I2 Realistic: power in > power out Efficiencies usually around 95%

Transformer Summary Power in  power out  loops  higher V, lower I  loops  lower V, higher I

Question A “step-down” transformer converts input at 120 V to output at 20 V. If the input circuit has 1100 W, how much power is available at the output? 200 W. 660 W. 1100 W. 2400 W.

General Physics L18_Faraday Group Work A transformer with 1000 primary windings converts AC at 110 V (primary) to 220 V (secondary). Which is greater: the voltage in the primary circuit or the voltage in the secondary circuit? Where will the number of loops be greater: in the primary or in the secondary?

Group Work A transformer with 1000 primary windings converts AC at 110 V (primary) to 220 V (secondary). What is the voltage ratio V2/V1? What is the loops ratio N2/N1? How many loops are in the secondary circuit (N2)?

Group Work A transformer with 1000 primary windings converts AC at 110 V (primary) to 220 V (secondary). What is the current ratio I2/I1?

Formulas for Transformers Loops: V1 V2 N1 N2 = Power: V1I1 = V2I2 Potential: V2 = V1 I1 I2 = V1 N2 N1 Current: I2 = I1 V1 V2 = I1 N1 N2

Example A transformer with 5000 primary coils and 100 secondary coils has an input voltage of 50 kV. What is the output voltage? Vout = Vin Nout/Nin = (50 kV)(100/5000) = (50 kV)/50 = 1 kv = 1,000 V